V Espanol A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in New York and Rhode Island. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of New York is greater than the mean annual income of childcare workers in Rhode Island. To see if this is true, the firm selected a random sample of 15 childcare workers from New York and an independent random sample of 15 childcare workers from Rhode Island and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars D New York 53715, 59120, 42861, 50350, 41606, 45910, 53416, 51880, 52330, 42748, 51789, 47897, 41775, 49582, 53366 Rhode Island 51559, 43806, 43169, 54144, 53586, 40928, 42956, 40814, 53987, 48749, 41652, 34661, 54882, 36245, 44457 Send data to calc... v Send data to Excel The population standard deviations for the annual incomes of childcare workers in New York and in Rhode Island are estimated as 6400 and 6600, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, u, of childcare workers in New York is greater than the mean annual income, ly, of childcare workers in Rhode Island? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H1. Ho : 0 S H :0 (b) Determine the type of test statistic to use. "=0 050 020 Choose one) 070 00 (c) Find the value of the test statistic. (Round to three or more decimal places.) X (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean annual income of childcare workers in New York is greater than the mean annual income of childcare workers in Rhode Island? Yes No